Medical Sciences: cram pack

Formula sheets, the key method steps for every topic and 14 practice problems, with full solutions at the back.

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1Formulas and methods

Arterial blood gas interpretation

Normal ranges
pH 7.35–7.45, PaCO₂ 35–45 mmHg (4.7–6.0 kPa), HCO₃⁻ 22–26 mmol/L
ROME
Respiratory: PaCO₂ opposite to pH; Metabolic: HCO₃⁻ equal to pH
Winter’s formula
PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2
Metabolic alkalosis
PaCO₂ ≈ 0.7·HCO₃⁻ + 21
Anion gap
AG = Na⁺ − (Cl⁻ + HCO₃⁻) ≈ 8–12
Albumin-corrected gap
AG + 2.5·(4.0 − alb g/dL) = AG + 0.25·(40 − alb g/L)
Delta ratio
(AG − 12)/(24 − HCO₃⁻)
P/F ratio
PaO₂/FiO₂
Alveolar gas equation
PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8
Serum osmolality
2·Na⁺ + glucose + urea (2·Na⁺ + glucose/18 + BUN/2.8)

Method

  1. Read the pH: below 7.35 is acidosis, above 7.45 alkalosis.
  2. Find the value that explains it: PaCO₂ moving opposite to the pH is respiratory, HCO₃⁻ moving with the pH is metabolic.
  3. Look at the other value: normal means uncompensated, abnormal in the compensating direction means partial compensation, and a normal pH with both abnormal means full compensation.
  4. In a metabolic acidosis, compare PaCO₂ with Winter’s formula, 1.5·HCO₃⁻ + 8 ± 2, and calculate the anion gap Na⁺ − (Cl⁻ + HCO₃⁻).
  5. Check a high anion gap with the delta ratio and, when albumin is low, with the corrected gap.

ECG rhythm strip interpretation

Paper (25 mm/s, 10 mm/mV)
1 small box = 0.04 s, 1 large box = 0.20 s, 10 mm = 1 mV
Heart rate, regular rhythm
300 ÷ large boxes = 1500 ÷ small boxes = 60 ÷ RR (s)
Heart rate, irregular rhythm
QRS complexes in 6 s × 10
Normal PR interval
0.12–0.20 s
Normal QRS duration
< 0.12 s
QTc (Bazett)
QT/√RR
QTc (Fridericia)
QT/∛RR
QTc (Framingham)
QT + 154·(1 − RR)
Sinus rates
bradycardia < 60, normal 60–100, tachycardia > 100 /min
Escape rates
junctional 40–60, ventricular 20–40 /min
Fast rhythms
SVT 150–250 /min (narrow), VT > 100 /min (wide)

Method

  1. Rate: for a regular rhythm divide 300 by the large boxes or 1500 by the small boxes between two R waves; for an irregular rhythm count the QRS complexes in 6 seconds and multiply by 10.
  2. Rhythm: compare the R–R intervals. Equal is regular; a repeating pattern is regularly irregular; no pattern at all is irregularly irregular.
  3. P waves: is there an upright P wave in lead II before every QRS, all alike? Look for fibrillatory or sawtooth waves, inverted P waves and P waves without a QRS.
  4. PR interval: from the start of P to the start of the QRS, normally 0.12–0.20 s and constant. Watch whether it lengthens, stays fixed before a dropped beat, or varies at random.
  5. QRS duration: below 0.12 s is narrow; 0.12 s or more is wide. Then name the rhythm, and for the QT use QTc = QT/√RR (Bazett) with times in seconds.

Evidence-based practice statistics

Sensitivity and specificity
Se = a/(a + c), Sp = d/(b + d)
Predictive values
PPV = a/(a + b), NPV = d/(c + d)
Accuracy
(a + d)/n
Likelihood ratios
LR+ = Se/(1 − Sp), LR− = (1 − Se)/Sp
PPV at prevalence p
Se·p / (Se·p + (1 − Sp)(1 − p))
Odds
odds = p/(1 − p); p = odds/(1 + odds); post-test odds = pre-test odds × LR
Risk measures
RR = EER/CER, ARR = CER − EER, RRR = ARR/CER
Number needed to treat
NNT = 1/ARR, rounded up; NNH = 1/(EER − CER)
Odds ratio
OR = ad/(bc)
Incidence rate
new cases / person-time

Method

  1. Draw the 2 × 2 table and label a, b, c and d before you calculate.
  2. Read sensitivity and specificity down the columns, predictive values along the rows.
  3. For another prevalence, imagine 10 000 people and fill the table with Se, Sp and the prevalence.
  4. For a likelihood ratio, convert the probability to odds, multiply, and convert back.
  5. For a trial, find EER and CER first; then RR = EER/CER, ARR = CER − EER and NNT = 1/ARR rounded up.

2Practice problems

1.Human anatomyMedium

Which structure produces most of the cerebrospinal fluid?

  1. AChoroid plexus
  2. BPia mater
  3. CArachnoid granulations
  4. DPineal gland
2.Human anatomyHard

After axillary lymph node surgery, a patient's scapula sticks out from the chest wall when pushing against a wall. Which nerve has been damaged?

  1. ASuprascapular nerve
  2. BAxillary nerve
  3. CLong thoracic nerve
  4. DThoracodorsal nerve
3.Human physiologyMedium

Why can cardiac muscle not be tetanised like skeletal muscle?

  1. AIt is controlled only by hormones
  2. BIts long refractory period lasts almost as long as the contraction
  3. CIt is not striated
  4. DIt has no calcium in the sarcoplasmic reticulum
4.Human physiologyHard

In long-standing aortic stenosis, how does the left ventricle adapt?

  1. AAtrophy of the muscle due to less work
  2. BThinning of the wall with dilation
  3. CNo change because the valve is not part of the ventricle
  4. DConcentric hypertrophy with a thicker wall
5.MicrobiologyMedium

Why are pregnant women advised to avoid unpasteurised soft cheeses?

  1. AThey may contain Listeria, which can harm the fetus
  2. BThey often contain the hepatitis C virus, which crosses the placenta
  3. CThey may contain tapeworm eggs
  4. DThey contain too much lactose for the fetus
6.MicrobiologyHard

What does an R0 (basic reproduction number) of 3 mean?

  1. AThree doses of vaccine are needed
  2. BThe infection lasts three days
  3. CThree percent of infected people die
  4. DOn average one case infects three others in a fully susceptible population
7.PharmacologyMedium

A patient starting sulfasalazine should be told about which harmless effect?

  1. AOrange-yellow colouring of the urine
  2. BWhite spots on the nails
  3. CBlue colouring of the tongue and gums
  4. DGreen colouring of the sweat
8.PharmacologyHard

The volume of distribution of a drug is very large (for example 500 L in an adult). What does this suggest?

  1. AThe drug is extensively taken up into tissues
  2. BThe drug stays almost entirely in the plasma compartment
  3. CThe drug is quickly excreted by the kidneys
  4. DThe drug cannot be given intravenously
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 149 mmol/L, glucose 16.6 mmol/L and urea 10.6 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 149 mmol/Lglucose 16.6 mmol/Lurea 10.6 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 31 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 31 mmol/L
PaCO₂ = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

Measure the QT interval and the R–R interval on this regular lead II strip, then calculate the rate-corrected QTc with Bazett’s formula QTc = QT/√RR (both in seconds). Give the answer in seconds to three decimals.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
QTc = s
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVventricular fibrillationasystolejunctional rhythmsinus bradycardia

Identify the rhythm on this lead II strip. Click your answer.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
  1. 1ventricular fibrillation
  2. 2asystole
  3. 3junctional rhythm
  4. 4sinus bradycardia
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment6194200abcontrol56744800cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 200 patients received a new treatment and 800 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the relative risk RR of the event with treatment. Round to two decimal places.

treatment: 6/200control: 56/800
RR =
14.Evidence-based practice statisticsHard
pre-test50%post-test?p′LR−

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 50% for a disease. A test with sensitivity 63% and specificity 85% comes back negative. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 50%Se = 63%Sp = 85%negative
p′ = %

3Solutions

1.Human anatomy

Answer: A · Choroid plexus

Why this is the answer

The choroid plexus in the ventricles secretes most CSF. CSF is reabsorbed into venous blood through the arachnoid granulations.

Answer

A · Choroid plexus
2.Human anatomy

Answer: C · Long thoracic nerve

Why this is the answer

The long thoracic nerve supplies serratus anterior, which holds the scapula against the chest wall. Damage causes a winged scapula.

Answer

C · Long thoracic nerve
3.Human physiology

Answer: B · Its long refractory period lasts almost as long as the contraction

Why this is the answer

The plateau of the cardiac action potential gives a long refractory period, so the muscle relaxes before it can be excited again. This allows the heart to refill.

Answer

B · Its long refractory period lasts almost as long as the contraction
4.Human physiology

Answer: D · Concentric hypertrophy with a thicker wall

Why this is the answer

Pressure overload makes the ventricular wall thicken (concentric hypertrophy) to keep wall stress normal. Volume overload, as in regurgitation, causes dilation instead.

Answer

D · Concentric hypertrophy with a thicker wall
5.Microbiology

Answer: A · They may contain Listeria, which can harm the fetus

Why this is the answer

Listeria monocytogenes can grow in chilled foods and cross the placenta. It can cause miscarriage, stillbirth or severe neonatal infection.

Answer

A · They may contain Listeria, which can harm the fetus
6.Microbiology

Answer: D · On average one case infects three others in a fully susceptible population

Why this is the answer

R0 is the average number of secondary cases from one case when everyone is susceptible. Herd immunity needs roughly 1 − 1/R0 of the population immune: about 67% for R0 = 3.

Answer

D · On average one case infects three others in a fully susceptible population
7.Pharmacology

Answer: A · Orange-yellow colouring of the urine

Why this is the answer

Sulfasalazine can colour urine and sometimes skin and contact lenses orange-yellow. More serious adverse effects include blood disorders and rash, so blood counts are monitored.

Answer

A · Orange-yellow colouring of the urine
8.Pharmacology

Answer: A · The drug is extensively taken up into tissues

Why this is the answer

A Vd far above total body water means the plasma concentration is low because most of the drug sits in tissues (for example fat or muscle), as with digoxin or amiodarone.

Answer

A · The drug is extensively taken up into tissues
9.Arterial blood gas interpretation

Answer: Osm = 325 mOsm/kg

Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.

Calculated osmolality

Osm = 2·149 + 16.6 + 10.6 = 325.2 ≈ 325 mOsm/kg

Answer

Osm = 325 mOsm/kg
10.Arterial blood gas interpretation

Answer: PaCO₂ = 42.7 mmHg

Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.

Expected PaCO₂

0.7·31 + 21 = 42.7 mmHg

Answer

PaCO₂ = 42.7 mmHg

The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.

11.ECG rhythm strip interpretation

Answer: QTc = 0.485 s

QT and QTc: the QT interval runs from the start of the QRS complex to the end of the T wave. It shortens as the heart rate rises, so it is corrected for rate with the R–R interval in seconds: Bazett QTc = QT/√RR and Fridericia QTc = QT/∛RR. Bazett is the formula most textbooks use; it over-corrects at fast rates, where Fridericia is preferred. Limits differ between references: a QTc above about 0.45 s in men or 0.46 s in women is usually called prolonged, and above 0.50 s markedly prolonged.

Measure

QT = 10 × 0.04 = 0.40 s
RR = 17 × 0.04 = 0.68 s

Bazett’s formula

QTc = 0.40/√0.68 = 0.40/0.8246 = 0.485 s

Answer

QTc = 0.485 s

Above the usual limits for both men (about 0.45 s) and women (about 0.46 s): prolonged. (485 ms)

12.ECG rhythm strip interpretation

Answer: asystole

Ventricular rhythms: ventricular tachycardia is a run of three or more wide (0.12 s or more) complexes in a row at more than 100/min, usually 150–250/min, regular, without related P waves. Ventricular fibrillation is a chaotic, irregular waveform with no identifiable P waves, QRS complexes or T waves and no countable rate. Asystole is an almost flat line with no ventricular activity; a flat line is always confirmed by checking the patient, the leads and the gain and a second lead. In resuscitation guidelines VF and pulseless VT are the shockable rhythms and asystole is not.

Five steps

1. Rate: no countable ventricular rate.
2. Rhythm: none; an almost flat line.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: no QRS complexes.

Interpretation

asystole

Answer

asystole

A flat line is always checked: look at the patient, the leads and the gain, and view a second lead, because a loose electrode or fine VF can look like asystole.

13.Evidence-based practice statistics

Answer: RR = 0.43

Likelihood ratios and risk measures: LR+ = sensitivity/(1 − specificity), LR− = (1 − sensitivity)/specificity. In a trial, EER and CER are the event rates with and without treatment: RR = EER/CER, ARR = CER − EER, RRR = ARR/CER and NNT = 1/ARR, rounded up. In a case-control study only the odds ratio OR = ad/(bc) can be used. An incidence rate = new cases/person-time.

Event rates

EER = 6/200 = 0.03
CER = 56/800 = 0.07

Relative risk

RR = 0.03/0.07 = 0.4286 ≈ 0.43

Answer

RR = 0.43
14.Evidence-based practice statistics

Answer: p′ = 30.3 %

Predictive values depend on prevalence: PPV = Se·p/(Se·p + (1 − Sp)(1 − p)) and NPV = Sp(1 − p)/(Sp(1 − p) + (1 − Se)p). With likelihood ratios: pre-test odds = p/(1 − p), post-test odds = pre-test odds × LR, probability = odds/(1 + odds). For a population of N, true positives = N·p·Se and false positives = N·(1 − p)·(1 − Sp). NNT = 1/(CER × RRR), rounded up.

Likelihood ratio

LR− = (1 − 0.63)/0.85 = 0.4353

Pre-test odds

0.5/(1 − 0.5) = 1

Post-test odds

1·0.4353 = 0.4353

Post-test probability

p′ = 0.4353/(1 + 0.4353) = 0.3033 ≈ 30.3%

Answer

p′ = 30.3%

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